中国1%人口抽样调查的不等概率重权数Bootstrap方差估计研究  

On Unequal Probability Rescaled Bootstrap Variance Estimation in China’s 1% Population Sampling Survey

作　　者：沈文静 杨贵军 孙玲莉 SHEN WENJING;YANG GUIJUN;SUN LINGLI(School of Statistics,Tianjin University of Finance and Economics,Tianjin 300222,China)

机构地区：[1]天津财经大学统计学院,天津300222

出　　处：《应用数学学报》2023年第1期1-20,共20页Acta Mathematicae Applicatae Sinica

基　　金：国家社科基金重大项目(22&ZD155);国家社科基金重点项目(20ATJ008);国家社科基金青年项目(20CTJ009);天津市统计科学研究项目(TJ2022KY0016)资助。

摘　　要：准确估计人口总数估计量方差是中国1%人口抽样调查数据分析重要内容.但由于中国1%人口抽样调查综合采用分层、二阶段、概率比例、整群抽样方法,且原则上从每个被抽中初级单元中仅抽取一个次级单元,传统抽样调查方差估计方法不再适用.本文提出适用于中国1%人口抽样调查的不等概率重权数Bootstrap方差估计法.该方法将不等概率抽样引入重抽样过程,并针对从绝大多数被抽中初级单元中仅抽取一个次级单元情形,设计入样概率.理论推导和数值模拟表明,新方法能减少方差估计量偏差,实例分析验证了该方法在中国1%人口抽样调查中的优良性.Constructing the variance estimator of the total population estimator is an important part of the data analysis in China’s 1% population sample survey.However,due to the stratified,two-stage,probability proportion,cluster sampling method used in China’s 1% population sampling survey,and in principle,only one secondary unit is selected from each selected primary unit,the traditional variance estimation method is no longer applicable.In order to improve the accuracy of variance estimation in population sampling survey,this paper proposes the unequal probability rescaled bootstrap.This method introduces unequal probability sampling into the re-sampling process,and redesigns the sampling probability for the case that only one secondary unit is selected from most primary units.Theoretical derivation and Monte Carlo simulation show that the new method can reduce the deviation of the variance estimator.An example analysis verifies the practical effectiveness of the method in China’s 1% population sampling survey.

关 键 词：中国1%人口抽样调查 不等概率重权数Bootstrap 方差估计 

分 类 号：O212.1[理学—概率论与数理统计] C924.25[理学—数学]